1. Field of the Invention
The invention relates to an ellipsometer for measuring the complex refractive index and thin film thickness of a sample.
2. Description of the Related Art
Currently, only ellipsometer widely applied in semiconductor, optical and chemical industries can measure the complex refractive index and thin film thickness of a sample with better precision and higher resolution. Ellipsometer which has been developed over 100 years includes null ellipsometer, rotating-polarizer ellipsometer, rotating-analyzer ellipsometer, rotating-compensator ellipsometer, phase-modulation ellipsometer, small-modulation ellipsometer, dual-modulation ellipsometer, analyzer-shifting ellipsometer, compound-splitting ellipsometer, phase-shifting ellipsometer, and phase-analysis ellipsometer.
The principle of the ellipsometer is based on the ellipsomeric polarizing optics. Typically, a planar wave electric field E can be divided into two electric fields Ep and Es. That is, the planar wave electric field E can be expressed by:
{right arrow over (E)}={right arrow over (E)}p+{right arrow over (E)}sxe2x80x83xe2x80x83(1)
With Jones"" vector, the electric field E can also be expressed by:                               E          ⇀                =                              [                          xe2x80x83                        ⁢                                                                                E                    p                                                                                                                    E                    s                                                                        ⁢                          xe2x80x83                        ]                    =                                    [                              xe2x80x83                            ⁢                                                                                                                  E                        op                                            ⁢                                              ⅇ                                                  j                          ⁡                                                      (                                                                                          ω                                ⁢                                                                  xe2x80x83                                                                ⁢                                t                                                            -                              kz                              -                                                              φ                                p                                                                                      )                                                                                                                                                                                                                                  E                        os                                            ⁢                                              ⅇ                                                  j                          ⁡                                                      (                                                                                          ω                                ⁢                                                                  xe2x80x83                                                                ⁢                                t                                                            -                              kz                              +                                                              φ                                s                                                                                      )                                                                                                                                                          ]                        ⁢                          xe2x80x83                        ∝                          [                              xe2x80x83                            ⁢                                                                                                                  E                        op                                            ⁢                                              ⅇ                        jΔ                                                                                                                                                        E                      os                                                                                  ⁢                              xe2x80x83                            ]                                                          (        2        )            
wherein Eop and Eos represent the amplitudes of the electric fields Ep and Es respectively, j={square root over (xe2x88x921)}, and xcex94=xcfx86pxe2x88x92xcfx86s. The traveling direction of the electric field E is along the z axis. If two polarized electric fields Eip and Eis are inputted, two outputted electric fields Erp and Ers can be measured after the two inputted electric fields Eip and Eis pass through a sample. Therefore, the related reflection coefficients can be given by:                               r          p                =                                            E              rp                                      E              ip                                =                                    ρ              p                        ⁢                          ⅇ                              jΔ                p                                                                        (        3        )                                          r          s                =                                            E              rp                                      E              ip                                =                                    ρ              s                        ⁢                          ⅇ                              jΔ                s                                                                        (        4        )            
wherein xcex94p represents the phase shift of the reflected electric field Ep, and xcex94s represents the phase shift of the reflected electric field Es. Thus, the polarization transfer function F (ellipsomeric function p) of the sample can be defined by:                     F        =                  ρ          =                                                                      E                  rP                                                  E                  rs                                                                              E                  ip                                                  E                  is                                                      =                                                                                E                    rp                                                        E                    ip                                                                                        E                    rs                                                        E                    is                                                              =                                                                    r                    p                                                        r                    s                                                  =                                                                                                    ρ                        p                                            ⁢                                              ⅇ                                                  jΔ                          p                                                                                                                                    ρ                        s                                            ⁢                                              ⅇ                                                  jΔ                          s                                                                                                      =                                      tan                    ⁢                                          xe2x80x83                                        ⁢                                          Ψⅇ                      jΔ                                                                                                                              (        5        )            
wherein       tan    ⁢          xe2x80x83        ⁢    Ψ    =            ρ      p              ρ      s      
xe2x80x83and xcex94=xcex94pxe2x88x92xcex94. The tan "psgr" and xcex94 are called ellipsomeric parameters.
Referring to FIG. 1, a general PMSA type ellipsometer is shown, wherein reference numeral 15 designates a polarizer having a pass axis angle b, 22 designates a phase modulator having m as the azimuth of a fast axis, 30 designates a sample, 42 designates an analyzer having a pass axis angle a, and 45 designates a detector. As shown in FIG. 1, a total of 6 parameters related to the four devices is the pass axis angle coordinate b of the polarizer P designated by a numeral 15, the azimuth angle m of the phase modulator M designated by a numeral 22, phase delay xcex4 of a phase retarder, the ellipsomeric parameters xcexa8, xcex94 and pass axis angle coordinate xcex1 of the analyzer A designated by a numeral 42. They can be expressed by Jones"" matrixes as follows:                     P        =                  [                      xe2x80x83                    ⁢                                                                                          cos                    2                                    ⁢                  b                                                                              sin                  ⁢                                      xe2x80x83                                    ⁢                  b                  ⁢                                      xe2x80x83                                    ⁢                  cos                  ⁢                                      xe2x80x83                                    ⁢                  b                                                                                                      sin                  ⁢                                      xe2x80x83                                    ⁢                  b                  ⁢                                      xe2x80x83                                    ⁢                  cos                  ⁢                                      xe2x80x83                                    ⁢                  b                                                                                                  sin                    2                                    ⁢                  b                                                              ⁢                      xe2x80x83                    ]                                    (        6        )                                M        =                  [                      xe2x80x83                    ⁢                                                                                                                ⅇ                                                                        i                          ⁢                                                      xe2x80x83                                                    ⁢                          δ                                                2                                                              ⁢                                          cos                      2                                        ⁢                    m                                    +                                                            ⅇ                                                                                                    -                            i                                                    ⁢                                                      xe2x80x83                                                    ⁢                          δ                                                2                                                              ⁢                                          sin                      2                                        ⁢                    m                                                                                                                    2                    ⁢                    i                    ⁢                                          xe2x80x83                                        ⁢                    sin                    ⁢                                          xe2x80x83                                        ⁢                    m                    ⁢                                          xe2x80x83                                        ⁢                    cos                    ⁢                                          xe2x80x83                                        ⁢                    m                    ⁢                                          xe2x80x83                                        ⁢                                          sin                      ⁡                                              (                                                  δ                          2                                                )                                                                              ⁢                                      xe2x80x83                                                                                                                        2                  ⁢                  i                  ⁢                                      xe2x80x83                                    ⁢                  sin                  ⁢                                      xe2x80x83                                    ⁢                  m                  ⁢                                      xe2x80x83                                    ⁢                  cos                  ⁢                                      xe2x80x83                                    ⁢                  m                  ⁢                                      xe2x80x83                                    ⁢                                      sin                    ⁡                                          (                                              δ                        2                                            )                                                                                                                                                              ⅇ                                                                                                    -                            i                                                    ⁢                                                      xe2x80x83                                                    ⁢                          δ                                                2                                                              ⁢                                          cos                      2                                        ⁢                    m                                    +                                                            ⅇ                                                                        i                          ⁢                                                      xe2x80x83                                                    ⁢                          δ                                                2                                                              ⁢                                          sin                      2                                        ⁢                    m                                                                                ⁢                      xe2x80x83                    ]                                    (        7        )                                          S          =                      [                          xe2x80x83                        ⁢                                                                                tan                    ⁢                                          xe2x80x83                                        ⁢                                          Ψⅇ                      jΔ                                                                                        0                                                                              0                                                  1                                                      ]                          ⁢                  xe2x80x83                                    (        8        )                                          A          =                      [                          xe2x80x83                        ⁢                                                                                                      cos                      2                                        ⁢                    a                                                                                        sin                    ⁢                                          xe2x80x83                                        ⁢                    a                    ⁢                                          xe2x80x83                                        ⁢                    cos                    ⁢                                          xe2x80x83                                        ⁢                    a                                                                                                                    sin                    ⁢                                          xe2x80x83                                        ⁢                    a                    ⁢                                          xe2x80x83                                        ⁢                    cos                    ⁢                                          xe2x80x83                                        ⁢                    a                                                                                                              sin                      2                                        ⁢                    a                                                                        ]                          ⁢                  xe2x80x83                                    (        9        )            
If the detector 45 has a linear response, a signal I measured after passing through the analyzer 42 can be expressed by:
I=G{right arrow over (E)}+out{right arrow over (E)}out=G(ASMP{right arrow over (E)}in,)+(ASMP{right arrow over (E)}in)xe2x80x83xe2x80x83(10)
According to xe2x80x9cImprovement of phase-modulated ellipsometryxe2x80x9d issued on xe2x80x9cReview of Scientific Instruentsxe2x80x9d, vol. 60, p.p. 65-77, by Acher, O., E. Bigan, formula (10) can be further expressed as:
I(xcex4)=G[I+Is sin(xcex4)+Ic cos(xcex4)]xe2x80x83xe2x80x83(11)
wherein Is and Ic represents the intensities of the electric fields Ep and Es, respectively.                               I          ⁡                      (            δ            )                          =                  G          [                      xe2x80x83                    ⁢                                                                                          (                                          1                      -                                              cos                        ⁢                                                  xe2x80x83                                                ⁢                        2                        ⁢                        Ψcos2                        ⁢                                                  xe2x80x83                                                ⁢                        a                                                              )                                    +                                      cos                    ⁢                                          xe2x80x83                                        ⁢                    2                    ⁢                    m                    ⁢                                          xe2x80x83                                        ⁢                    cos                    ⁢                                          xe2x80x83                                        ⁢                    2                    ⁢                                          (                                              m                        -                        b                                            )                                        ⁢                                          (                                                                        cos                          ⁢                                                      xe2x80x83                                                    ⁢                          2                          ⁢                          a                                                -                                                  cos                          ⁢                                                      xe2x80x83                                                    ⁢                          2                          ⁢                          Ψ                                                                    )                                                        +                                                                                                      sin                  ⁢                                      xe2x80x83                                    ⁢                  2                  ⁢                  a                  ⁢                                      xe2x80x83                                    ⁢                  cos                  ⁢                                      xe2x80x83                                    ⁢                  Δsin2Ψsin2                  ⁢                                      xe2x80x83                                    ⁢                  m                  ⁢                                      xe2x80x83                                    ⁢                  cos                  ⁢                                      xe2x80x83                                    ⁢                  2                  ⁢                                      (                                          m                      -                      b                                        )                                                                                ⁢                      xe2x80x83                    ]                                    (        12        )            xe2x80x83Is=xe2x88x92 sin 2xcexa8 sin 2a sin 2(mxe2x88x92b)sin xcex94xe2x80x83xe2x80x83(13)
Ic=xe2x88x92 sin 2(mxe2x88x92b)[sin 2m(cos 2xcexa8xe2x88x92 cos 2a)+sin 2xcexa8 cos 2m cos xcex94]xe2x80x83xe2x80x83(14)
Constant G is determined by the sensitivity of the detector 45, linear circuit amplification ratio and the ellipsomeric parameters. If any one of the parameters P, M, xcex4 and A is modulated by time, then using a lock-in amplifier, the ellipsomeric parameters "psgr", xcex94 and G can be obtained from formula (11). The thickness of the sample can then be estimated.
The phase-shifting ellipsometer having the prior PMSA configuration employs a phase modulator to shift the phase of light to 0, xcfx80/2, and xcfx80 respectively, so as to measure the ellipsomeric parameters.
The only difference between the phase-analysis ellipsometer and the phase-shifting ellipsometer is that the polarizer, phase modulator, analyzer, etc. have different angle parameters. With above mentioned angle parameters, the reflection coefficients rp, rs of the electric fields Ep, Es can be measured directly. Meanwhile, analysis can be performed using methods well-known in prior art phase-analysis ellipsometers.
In view of the above, the invention is to provide an ellipsometer for measuring the complex refractive index and thin film thickness of a sample, which not only has all complete functions like the conventional ellipsometer, but also is small in volume, can precisely control the angle and direction of an incident light beam with respect to a sample and is easy to use. Moreover, without employing additional and details calibration procedures typically needed for traditional ellipsometers, the ellipsometer disclosed in this invention can be widely applied in semiconductor, optical and chemical industries for measuring the complex refractive index and thin film thickness of the sample.
A first ellipsometer for measuring the complex refractive index and thin film thickness of a sample according to the invention includes a linear polarized light source used to generate a measuring beam for probing the sample; a phase modulator used to control the phase of the measuring beam thereby to generate a sampling beam; a reference analyzer used to generate a reference beam according to part of the sampling beam thereby to adjust the intensity of the sampling beam; a polarization analyzer used to analyze the phase, polarization and intensity of the sampling beam after the sampling beam is reflected by the sample; and a light direction controller used to control the incident angle and direction of the sampling beam with respect to the sample, wherein the sampling beam is reflected by the sample to enter the light direction controller, and thereafter the sampling beam is reflected by the light direction controller and re-reflected by the sample to enter the polarization analyzer along an original optical path, but toward an opposite direction.
A second ellipsometer for measuring the complex refractive index and thin film thickness of a sample according to the invention includes a linear polarized light source used to generate a measuring beam for probing the sample; a phase modulator used to control the phase of the measuring beam thereby to generate a sampling beam; a reference analyzer used to generate a reference beam according to part of the sampling beam to adjust the intensity of the sampling beam; a polarization analyzer used to analyze the phase, polarization and intensity of the sampling beam after the sampling beam is reflected by the sample; and a light direction controller used to control the incident angle and direction of the sampling beam with respect to the sample, wherein the sampling beam is reflected by the sample to enter the light direction controller, and thereafter the sampling beam is reflected by the light direction controller and re-reflected by the sample to enter the polarization analyzer along an original optical path, but toward an opposite direction; and an ellipsomeric parameter calibrator used to replace the sample to allow the sampling beam be perpendicularly incident to the surface of the ellipsomeric parameter calibrator and perpendicularly reflected when the ellipsomeric parameters of the phase modulator, the reference analyzer and the polarization analyzer are calibrated.
A third ellipsometer for measuring the complex refractive index and thin film thickness of a sample through a transparent or translucent medium according to the invention includes a linear polarized light source used to generate a measuring beam for probing the sample; a phase modulator used to control the phase of the measuring beam thereby to generate a sampling beam; a reference analyzer used to generate a reference beam according to part of the sampling beam to adjust the intensity of the sampling beam; a polarization analyzer used to analyze the phase, polarization and intensity of the sampling beam after the sampling beam is reflected by the sample; and a light direction controller used to control the incident angle and direction of the sampling beam with respect to the sample, wherein the sampling beam is reflected by the sample to enter the light direction controller through the medium, and thereafter the sampling beam is reflected by the light direction controller to pass through the medium and re-reflected by the sample to enter the polarization analyzer along an original optical path, but toward an opposite direction
A fourth ellipsometer for measuring the complex refractive index and thin film thickness of a sample through a transparent or translucent medium according to the invention includes a linear polarized light source used to generate a measuring beam for probing the sample; a phase modulator used to control the phase of the measuring beam thereby to generate a sampling beam; a reference analyzer used to generate a reference beam according part of the sampling beam to adjust the intensity of the sampling beam; a polarization analyzer used to analyze the phase, polarization and intensity of the sampling beam after the sampling beam is reflected by the sample; a light direction controller used to control the incident angle and direction of the sampling beam with respect to the sample, wherein the sampling beam is reflected by the sample to enter the light direction controller through the medium, and thereafter the sampling beam is reflected by the light direction controller to pass through the medium and re-reflected by the sample to enter the polarization analyzer along an original optical path, but toward an opposite direction; and an ellipsomeric parameter calibrator used to replace the sample to allow the sampling beam be perpendicularly incident to the surface of the ellipsomeric parameter calibrator and perpendicularly reflected when the ellipsomeric parameters of the phase modulator, the reference analyzer, the polarization analyzer and the medium are calibrated.